# Causally Abstracted Multi-armed Bandits

arXiv: https://arxiv.org/abs/2404.17493 · HTML: https://mlsanity.com/paper/2404.17493/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 59 references that are in the map.
- First posted on arXiv 26 Apr 2024.

## Builds on (most cited first, 30 of 33)

- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Bandits and Experts in Metric Spaces](https://mlsanity.com/paper/1312.1277/) (2013)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Lipschitz Bandits: Regret Lower Bounds and Optimal Algorithms](https://mlsanity.com/paper/1405.4758/) (2014)
- [Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits](https://mlsanity.com/paper/1904.00242/) (2019)
- [A Simple Approach for Non-stationary Linear Bandits](https://mlsanity.com/paper/2103.05324/) (2021)
- [The End of Optimism? An Asymptotic Analysis of Finite-Armed Linear Bandits](https://mlsanity.com/paper/1610.04491/) (2016)
- [Minimal Exploration in Structured Stochastic Bandits](https://mlsanity.com/paper/1711.00400/) (2017)
- [Causal Bayesian Optimization](https://mlsanity.com/paper/2005.11741/) (2020)
- [Sequential Transfer in Multi-armed Bandit with Finite Set of Models](https://mlsanity.com/paper/1307.6887/) (2013)
- [Budgeted and Non-budgeted Causal Bandits](https://mlsanity.com/paper/2012.07058/) (2020)
- [Causal Effect Identification in Cluster DAGs](https://mlsanity.com/paper/2202.12263/) (2022)
- [Multi-Armed Bandits with Correlated Arms](https://mlsanity.com/paper/1911.03959/) (2019)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Adaptively Exploiting d-Separators with Causal Bandits](https://mlsanity.com/paper/2202.05100/) (2022)
- [Combinatorial Causal Bandits](https://mlsanity.com/paper/2206.01995/) (2022)
- [Bounded Regret for Finite-Armed Structured Bandits](https://mlsanity.com/paper/1411.2919/) (2014)
- [Abstraction between Structural Causal Models: A Review of Definitions and Properties](https://mlsanity.com/paper/2207.08603/) (2022)
- [Optimal Learning for Structured Bandits](https://mlsanity.com/paper/2007.07302/) (2020)
- [Multi-task Causal Learning with Gaussian Processes](https://mlsanity.com/paper/2009.12821/) (2020)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Multi-Armed Bandits with Dependent Arms](https://mlsanity.com/paper/2010.09478/) (2020)
- [On conditional versus marginal bias in multi-armed bandits](https://mlsanity.com/paper/2002.08422/) (2020)

## Built on by (most cited first, 6 of 6)

- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Distributionally Robust Causal Abstractions](https://mlsanity.com/paper/2510.04842/) (2025)
- [Identifiability in Causal Abstractions: A Hierarchy of Criteria](https://mlsanity.com/paper/2507.06213/) (2025)
- [Using causal abstractions to accelerate decision-making in complex bandit problems](https://mlsanity.com/paper/2509.04296/) (2025)
- [Causal Effect Identifiability in Causal Abstractions: A Strict Hierarchy of Criteria](https://mlsanity.com/paper/2610.13520/) (2026)

## Abstract (arXiv)

Multi-armed bandits (MAB) and causal MABs (CMAB) are established frameworks for decision-making problems. The majority of prior work typically studies and solves individual MAB and CMAB in isolation for a given problem and associated data. However, decision-makers are often faced with multiple related problems and multi-scale observations where joint formulations are needed in order to efficiently exploit the problem structures and data dependencies. Transfer learning for CMABs addresses the situation where models are defined on identical variables, although causal connections may differ. In this work, we extend transfer learning to setups involving CMABs defined on potentially different variables, with varying degrees of granularity, and related via an abstraction map. Formally, we introduce the problem of causally abstracted MABs (CAMABs) by relying on the theory of causal abstraction in order to express a rigorous abstraction map. We propose algorithms to learn in a CAMAB, and study their regret. We illustrate the limitations and the strengths of our algorithms on a real-world scenario related to online advertising.